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Examining the Feasibility of the Sturm–Liouville Theory for Ross Recovery

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  • Shinmi Ahn

    (Graduate School, Kyung Hee University, 6, Kyungheedae-ro, Dongdaemun-gu, Seoul 02453, Korea)

  • Hyungbin Park

    (Department of Mathematical Sciences and RIMS, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, Korea)

Abstract

Recent studies have suggested that it is feasible to recover a physical measure from a risk-neutral measure. Given a market state variable modeled as a Markov process, the key concept is to extract a unique positive eigenfunction of the generator of the Markov process. In this work, the feasibility of this recovery theory is examined. We prove that, under a restrictive integrability condition, recovery is feasible if and only if both endpoints of the state variable are limit-point. Several examples with explicit positive eigenfunctions are considered. However, in general, a physical measure cannot be recovered from a risk-neutral measure. We provide a financial and mathematical rationale for such recovery failure.

Suggested Citation

  • Shinmi Ahn & Hyungbin Park, 2020. "Examining the Feasibility of the Sturm–Liouville Theory for Ross Recovery," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:550-:d:343184
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    References listed on IDEAS

    as
    1. Gurdip Bakshi & Fousseni Chabi-Yo & Xiaohui Gao, 2018. "A Recovery that We Can Trust? Deducing and Testing the Restrictions of the Recovery Theorem," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 532-555.
    2. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    3. Dillschneider, Yannick & Maurer, Raimond, 2019. "Functional Ross recovery: Theoretical results and empirical tests," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    4. repec:oup:rfinst:v:21:y:2017:i:4:p:1403-1444. is not listed on IDEAS
    5. Hyungbin Park, 2016. "Ross recovery with recurrent and transient processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(5), pages 667-676, May.
    6. Likuan Qin & Vadim Linetsky, 2016. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing," Operations Research, INFORMS, vol. 64(1), pages 99-117, February.
    7. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    8. Johan Walden, 2017. "Recovery with Unbounded Diffusion Processes," Review of Finance, European Finance Association, vol. 21(4), pages 1403-1444.
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